How do I add a new Global Variable?

Hard to say without seeing an error message.

I still think it would be easier to do this in a custom module. Put these 2 files in a new folder called sites/all/modules/mymodule

mymodule.info:

name = Mymodule
description = Does something to do with mapping visitors' IP addresses to location.
version = 0.1

mymodule.module:

/**
 * Implementation of hook_init()
 *
 * This is called near the beginning of each page request.
 * If $_SESSION['location'] is not set then populate it with location info based on visitor IP address.
 */
function mymodule_init() {
  if(isset($_SESSION['location'])) {
    // Possibly do something, or maybe just do it on the relevant pages rather than here
  }
  else {
    // If necessary could also check that we are on a landing page, but maybe no harm to do it always
    $_SESSION['location'] = mymodule_get_location();
  }
}

/**
 * Get visitor location based on IP address
 */
function mymodule_get_location() {
  do_something_with($_SERVER['REMOTE_ADDR']);
}

N.B.
1. Drupal handles all the session stuff automatically during its bootstrap phase.
2. This script will run with the main Drupal folder as cwd.
3. If necessary you could use taxonomy to "tag" those pages (landing pages) you want this script running on and put that test in the code above. A more basic way would just be to check the node number or node type.

gpk
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